The co - efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = aT, where a is a constant and T in ºC. If the length of the rod is ℓ at temperature 0ºC, then the temperature at which the length will be 2ℓ is :

Engineering

Physics

Thermal Expansion

Question

$\sqrt{\frac{ℓn 2}{a}}$

$\sqrt{\frac{ℓn 4}{a}}$

$\sqrt{\frac{2 ℓ}{a}}$

$\sqrt{\frac{ℓ}{a}}$

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$dℓ = ℓ \propto \frac{d}{T} T \Rightarrow \frac{dℓ}{ℓ} = \int_{0}^{T} αdT$

$l n 2 = \frac{{aT}^{2}}{2} \Rightarrow T = \sqrt{\frac{l n 4}{a}}$ .